The weekly proportion of storage tank capacity that is utilized at a regional hazardous liquid waste receiving site is an outcome of a \(\operatorname{Beta}(\theta, 1)\) random variable. At the end of each week the storage tank is emptied. A random sample of a year's worth of observations of capacity utilization at the site produced the results displayed in the table below, reported in sequence row-wise.

(a) Define a GLR size \(\alpha\) test of \(H_{0}: \theta=\theta_{0}\) versus \(H_{0}: \theta eq \theta_{0}\).

(b) Test the hypothesis that the expected weekly storage tank capacity utilized is equal to 5 at a significance level of .95. If the exact distribution of the GLR test appears to be intractable, then use an asymptotic test.

(c) Test that the observations can be interpreted as a random sample from some population distribution. Use a size .05 test.

Transcribed Image Text:

0.148 0.501 0.394 0.257 0.759 0.763 0.092 0.155 0.409 0.257 0.586 0.919 0.278 0.076 0.019 0.513 0.123 0.390 0.030 0.082 0.935 0.607 0.075 0.729 0.664 0.802 0.338 0.539 0.055 0.984 0.269 0.679 0.382 0.549 0.069 0.028 0.770 0.296 0.105 0.465 0.194 0.675 0.696 0.068 0.091 0.132 0.156 0.050 0.477 0.754 0.164 0.527